Disorder-induced topology in quench dynamics

We study the effect of strong disorder on topology and entanglement in quench dynamics. Although disorder-induced topological phases have been well studied in equilibrium, the disorder-induced topology in quench dynamics has not been explored. In this work, we predict a disorder-induced topology of post-quench states characterized by the quantized dynamical Chern number and the crossings in the entanglement spectrum in $(1+1)$ dimensions. The dynamical Chern number undergoes transitions from zero to unity, and back to zero when increasing the disorder strength. The boundaries between different dynamical Chern numbers are determined by delocalized critical points in the post-quench Hamiltonian with the strong disorder. An experimental realization in quantum walks is discussed.